2020/01/31 by Fabienne Comte, Nicolas Marie
Engineering · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Bandwidth (computing) #Computer science #Consistent estimator #Control Systems and Identification #Discrete mathematics #Estimator #Invariant estimator #Kernel (algebra) #Kernel regression #Mathematics #Minimum-variance unbiased estimator #Regression #Statistical Methods and Inference #Statistics #Stein's unbiased risk estimate #math.ST #msc:62G05 #msc:62G08 #stat.TH
paper · pdf · doi:10.1214/21-ejs1849
published as Electronic Journal of Statistics 15, 1, 2566-2607, 2021 · 43 pages
openalex publication_date 2021/01/01 · arxiv created 2021/04/25 · arxiv updated 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for both data driven estimators and for the resulting ratio. The simulation study confirms that both estimators have good performances, compared to the ones obtained by cross-validation selection of the bandwidth. However, unexpectedly, the single-bandwidth cross-validation estimator is found to be much better than the ratio of the previous two good estimators, in the small noise context. However, the two methods have similar performances in models with large noise.